**Direct Proportion**

Direct proportion is the relationship between two variables whose ratio is equal to a constant value. In other words, direct proportion is a situation where an increase (or decrease) in one quantity causes a corresponding increase (or decrease) in the other quantity.

Mathematically, two quantities *x *and *y *are said to be in **direct proportion **if they increase (decrease) together in such a manner that the ratio of their corresponding values remains constant.

In other words, if (*x* / *y*) = *m* or *x* = *my* [*m *is a positive number], then *x *and *y *are said to vary directly. In such a case if *y*_{1}, *y*_{2} are the values of *y *corresponding to the values *x*_{1}, *x*_{2} of *x *respectively then (*x*_{1} / *y*_{1}) = (*x*_{2} / *y*_{2}). When two quantities *x *and *y *are in direct proportion (or vary directly) they are also written as *x *∞ *y*.

Let’s take some real life examples of direct proportion.

(**a**) The cost of rice is directly proportional to the weight. This means that, if the quantity of rice increase (or decrease), the price will also increase (or decrease).

(**b**) Work done is directly proportional to the number of workers. This means that, more workers, more work and les workers, less work accomplished.

(**c**) The fuel consumption of a car is proportional to the distance covered. This means that, more workers, more work and les workers, less work accomplished.

**Inverse Proportion**

Inverse proportion is the relationship between two variables whose product is equal to a constant value. In other words, direct proportion is a situation where an increase (or decrease) in one quantity causes a corresponding decrease (or increase) in the other quantity.

Mathematically, two quantities *x *and *y *are said to be in **inverse proportion **if an increase in *x *causes a proportional decrease in *y *(and vice-versa) in such a manner that the product of their corresponding values remains constant.

In other words, if *xy* = *m* [*m *is a positive number], then *x *and *y *are said to vary inversely. In such a case if *y*_{1}, *y*_{2} are the values of *y *corresponding to the values *x*_{1}, *x*_{2} of *x *respectively then *x*_{1 }*y*_{1} = *x*_{2} *y*_{2}. When two quantities *x *and *y *are in inverse proportion (or vary inversely) they are also written as *x *∞ (1 / *y*).

Let’s take some real life examples of inverse proportion.

(**a**) As the number of workers increases, time taken to finish the job decreases.

(**b**) If we increase the speed of a vehicle, the time taken to cover a given distance decreases.

(**c**) Cost of a book and number of books purchased in a fixed amount are inversely proportional.